Number of ways a world series can occur?

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The discussion focuses on calculating the number of ways a World Series can occur, where a team must win four games out of seven to claim victory. Participants explore the use of a tree diagram to represent the outcomes, questioning whether to depict wins and losses for a single team or between two competing teams. The conversation emphasizes that the winning team must win exactly four games, while the losing team can win up to three games, leading to a combinatorial analysis of game outcomes. The assumption is made that the order of wins and losses matters, particularly in calculating the arrangements of games played.

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Question says: Use a tree diagram to find the number of ways that the World Series can occur, where the first team that wins four games out of seven wins the series.

Is my tree diagram between a single team wining and losing? Or is it between team A winning or team B winning. This diagram keeps on going and when it ends there is barely any space left. How can I simplify this? Am I missing a way to cut it down shorter. Does losing twice in a row get you out or something?
 
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The winning team wins exactly 4 times. How many games can the losing team win? Then multiply this by two, since either team can be the winning team.

This assumes order doesn't matter. If it does, for each of the ways the loosing team can win a game, compute the number of ways to order the the remaining games, given that the winning team always wins the last game.
 

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